Air normally does not conduct electricity. However, if the
voltage is high enough (for a given amount of air) the electrical energy
causes the air atoms and molecules  composed of electrons, neutrons and
protons  to let go of their electrons.
This is called ionization. Because the electrons are negatively charged,
they are immediately attracted to the positive electrode and this movement
produces an electrical current. The electrons bump into other atoms along
the way, causing further ionization and therefore greater current. The
ions are constantly moving about, and this movement of charge produces
changing electric and magnetic fields that create the radio wave energy.
Most of the energy is produced as heat and light but a little goes to
form the radio wave energy we need for transmitting. The spark is not
a very efficient way of generating radio wave energy, but it is the simplest!

A conductor in its
natural state  negative electrons (blue)and positive ions (red) evenly
distributed along its length.

The same conductor
in a state of imbalance where all thenegative particles (blue) have been
forced to one end.